#!/usr/bin/env nickle

/*
 * Pressure Sensor Model, version 1.1
 *
 * written by Holly Grimes
 *
 * Uses the International Standard Atmosphere as described in
 *   "A Quick Derivation relating altitude to air pressure" (version 1.03)
 *    from the Portland State Aerospace Society, except that the atmosphere
 *    is divided into layers with each layer having a different lapse rate.
 *
 * Lapse rate data for each layer was obtained from Wikipedia on Sept. 1, 2007
 *    at site <http://en.wikipedia.org/wiki/International_Standard_Atmosphere
 *
 * Height measurements use the local tangent plane.  The postive z-direction is up.
 *
 * All measurements are given in SI units (Kelvin, Pascal, meter, meters/second^2).
 *   The lapse rate is given in Kelvin/meter, the gas constant for air is given
 *   in Joules/(kilogram-Kelvin).
 */

const real GRAVITATIONAL_ACCELERATION = -9.80665;
const real AIR_GAS_CONSTANT = 287.053;
const int NUMBER_OF_LAYERS = 7;
const real MAXIMUM_ALTITUDE = 84852;
const real MINIMUM_PRESSURE = 0.3734;
const real LAYER0_BASE_TEMPERATURE = 288.15;
const real LAYER0_BASE_PRESSURE = 101325;

/* lapse rate and base altitude for each layer in the atmosphere */
const real[NUMBER_OF_LAYERS] lapse_rate = {
	-0.0065, 0.0, 0.001, 0.0028, 0.0, -0.0028, -0.002
};
const int[NUMBER_OF_LAYERS] base_altitude = {
	0, 11000, 20000, 32000, 47000, 51000, 71000
};


/* outputs atmospheric pressure associated with the given altitude. altitudes
   are measured with respect to the mean sea level */
real altitude_to_pressure(real altitude) {
 
   real base_temperature = LAYER0_BASE_TEMPERATURE;
   real base_pressure = LAYER0_BASE_PRESSURE;

   real pressure;
   real base; /* base for function to determine pressure */
   real exponent; /* exponent for function to determine pressure */
   int layer_number; /* identifies layer in the atmosphere */
   int delta_z; /* difference between two altitudes */
   
   if (altitude > MAXIMUM_ALTITUDE) /* FIX ME: use sensor data to improve model */
      return 0;

   /* calculate the base temperature and pressure for the atmospheric layer
      associated with the inputted altitude */
   for(layer_number = 0; layer_number < NUMBER_OF_LAYERS - 1 && altitude > base_altitude[layer_number + 1]; layer_number++) {
      delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
      if (lapse_rate[layer_number] == 0.0) {
         exponent = GRAVITATIONAL_ACCELERATION * delta_z 
              / AIR_GAS_CONSTANT / base_temperature;
         base_pressure *= exp(exponent);
      }
      else {
         base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
         exponent = GRAVITATIONAL_ACCELERATION / 
              (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
         base_pressure *= pow(base, exponent);
      }
      base_temperature += delta_z * lapse_rate[layer_number];
   }

   /* calculate the pressure at the inputted altitude */
   delta_z = altitude - base_altitude[layer_number];
   if (lapse_rate[layer_number] == 0.0) {
      exponent = GRAVITATIONAL_ACCELERATION * delta_z 
           / AIR_GAS_CONSTANT / base_temperature;
      pressure = base_pressure * exp(exponent);
   }
   else {
      base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
      exponent = GRAVITATIONAL_ACCELERATION /
           (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
      pressure = base_pressure * pow(base, exponent);
   } 

   return pressure;
}


/* outputs the altitude associated with the given pressure. the altitude
   returned is measured with respect to the mean sea level */
real pressure_to_altitude(real pressure) {

   real next_base_temperature = LAYER0_BASE_TEMPERATURE;
   real next_base_pressure = LAYER0_BASE_PRESSURE;

   real altitude;
   real base_pressure;
   real base_temperature;
   real base; /* base for function to determine base pressure of next layer */
   real exponent; /* exponent for function to determine base pressure
                             of next layer */
   real coefficient;
   int layer_number; /* identifies layer in the atmosphere */
   int delta_z; /* difference between two altitudes */

   if (pressure < 0)  /* illegal pressure */
      return -1;
   if (pressure < MINIMUM_PRESSURE) /* FIX ME: use sensor data to improve model */
      return MAXIMUM_ALTITUDE;

   /* calculate the base temperature and pressure for the atmospheric layer
      associated with the inputted pressure. */
   layer_number = -1;
   do {
      layer_number++;
      base_pressure = next_base_pressure;
      base_temperature = next_base_temperature;
      delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
      if (lapse_rate[layer_number] == 0.0) {
         exponent = GRAVITATIONAL_ACCELERATION * delta_z 
              / AIR_GAS_CONSTANT / base_temperature;
         next_base_pressure *= exp(exponent);
      }
      else {
         base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
         exponent = GRAVITATIONAL_ACCELERATION / 
              (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
         next_base_pressure *= pow(base, exponent);
      }
      next_base_temperature += delta_z * lapse_rate[layer_number];
   }
   while(layer_number < NUMBER_OF_LAYERS - 1 && pressure < next_base_pressure);

   /* calculate the altitude associated with the inputted pressure */
   if (lapse_rate[layer_number] == 0.0) {
      coefficient = (AIR_GAS_CONSTANT / GRAVITATIONAL_ACCELERATION) 
                                                    * base_temperature;
      altitude = base_altitude[layer_number]
                    + coefficient * log(pressure / base_pressure);
   }
   else {
      base = pressure / base_pressure;
      exponent = AIR_GAS_CONSTANT * lapse_rate[layer_number] 
                                       / GRAVITATIONAL_ACCELERATION;
      coefficient = base_temperature / lapse_rate[layer_number];
      altitude = base_altitude[layer_number]
                      + coefficient * (pow(base, exponent) - 1);
   }

   return altitude;
}

real feet_to_meters(real feet)
{
    return feet * (12 * 2.54 / 100);
}

real meters_to_feet(real meters)
{
    return meters / (12 * 2.54 / 100);
}

/*
 * Values for our MP3H6115A pressure sensor
 *
 * From the data sheet:
 *
 * Pressure range: 15-115 kPa
 * Voltage at 115kPa: 2.82
 * Output scale: 27mV/kPa
 *
 * 
 * 27 mV/kPa * 2047 / 3300 counts/mV = 16.75 counts/kPa
 * 2.82V * 2047 / 3.3 counts/V = 1749 counts/115 kPa
 */

real counts_per_kPa = 27 * 2047 / 3300;
real counts_at_101_3kPa = 1674;

real count_to_kPa(real count)
{
	return (count / 2047 + 0.095) / 0.009;
}
typedef struct {
	int	type;
	int	time;
	int	a;
	int	b;
} flight_record;

flight_record
read_record(file in) {
	flight_record	r;
	File::fscanf(in, "%c %x %x %x\n",
	       &r.type, &r.time, &r.a, &r.b);
	return r;
}

real g_count = 264.8;
real
count_to_g(real count)
{
	return (15792 + g_count - count) / g_count;
}

real base_alt = 0;
real base_sec = 0;
real last_alt;
real last_sec;
real last_alt_speed;
real accel_speed;
real accel_meters;

real[...]	barometer;
real[...]	accelerometer;

real sinc(real x) = x != 0 ? sin(x)/x : 1;

real gaussian(real x) = exp(-(x**2)/2) / sqrt(2 * pi);

load "/usr/share/nickle/examples/kaiser.5c"

real[...] convolve(real[...] d, real[...] e) {
	real sample(n) = n < 0 ? d[0] : n >= dim(d) ? d[dim(d)-1] : d[n];
	real w = (dim(e) - 1) / 2;
	real c(int center) {
		real	v = 0;
		for (int o = -w; o <= w; o++)
			v += sample(center + o) * e[o + w];
		return v;
	}
	return (real[dim(d)]) { [n] = c(n) };
}

real sum(real[...] x) { real s = 0; for(int i = 0; i < dim(x); i++) s += x[i]; return s; }

real[...] filter(real[...] d, int half_width) {
#	real[half_width * 2 + 1] fir = { [n] = sinc(2 * pi * n / (2 * half_width)) };
	real M = half_width * 2 + 1;
	real[M] fir = { [n] = kaiser(n, M, 8) };
	real fir_sum = sum(fir);
	for (int i = 0; i < dim(fir); i++) fir[i] /= fir_sum;
	return convolve(d, fir);
}

real gravity = 9.80665;

real[...] pressure_value, accelerometer_value;
real[...] clock;

void readsamples(file in) {
	setdim(pressure_value, 0);
	setdim(accelerometer_value, 0);
	while (!File::end(in)) {
		flight_record r = read_record(in);
		if (r.type == 'A') {
			clock[dim(clock)] = r.time / 100;
			pressure_value[dim(pressure_value)] = r.b;
			accelerometer_value[dim(accelerometer_value)] = r.a;
		}
	}
}

readsamples(stdin);

int size = dim(accelerometer_value);
real[size] accelerometer = { [n] = gravity * (count_to_g(accelerometer_value[n]) - 1.0) };
real[size] barometer = { [n] = pressure_to_altitude(count_to_kPa(pressure_value[n] / 16) * 1000) };
real[size] filtered_accelerometer = filter(accelerometer, 8);
real[size] filtered_barometer = filter(barometer, 128);

real[...] integrate(real[...] d) {
	real[dim(d)] ret;
	for (int i = 0; i < dim(ret); i++)
		ret[i] = i == 0 ? 0 : ret[i-1] + (d[i-1] + d[i]) / 2 * (clock[i] - clock[i-1]);
	return ret;
}

real[...] differentiate(real[...] d) {
	real[dim(d)] ret;
	for (int i = 1; i < dim(ret); i++)
		ret[i] = (d[i] - d[i-1]) / (clock[i] - clock[i-1]);
	ret[0] = ret[1];
	return ret;
}

real[size] accel_speed = integrate(filtered_accelerometer);
real[size] accel_pos = integrate(accel_speed);
real[size] baro_speed = differentiate(filtered_barometer);
real[size] baro_accel = differentiate(baro_speed);

for (int i = 0; i < size; i++)
	printf("%g %g %g %g %g %g %g %g %g\n",
	       clock[i] - clock[0],
	       filtered_barometer[i] - filtered_barometer[0], accel_pos[i],
	       baro_speed[i], accel_speed[i],
	       baro_accel[i], filtered_accelerometer[i],
	       barometer[i] - barometer[0], accelerometer[i]);